There's quite a lot of presidents not born in the state they ran from.
The Vice Presidents are more exotic. One was born in Paris, and another in Ceylon, and one died in Berlin.
What!? You sure you're not thinking of First Ladies or something? Vice Presidents, like Presidents, are required by the constitution to be native born or have immigrated to the US before 1789.
I've also been through the biographies of US vice presidents and I've not found any such reference.
(I have found reference to a -baseless- conspiracy theory that Chester A Arthur was really his older brother, who was born in Canada.)
It's possible that someone could be born in another country and still become President or Vice President, as long as they were a US citizen by birth. If your parents were vacationing overseas or temporarily living overseas, for example, but were still both US citizens.
So that could have been the case with the VPs born in Paris and Ceylon (which ones were they, BTW?)